Can we connect to external api through Salesforce Professional Edition?
if not is there any other way around from only professional edition?
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Professional Edition doesn't allow APEX Classes even with some of the upgrades you can get, so you might be out of luck there. If that is the route you were planning on taking, the only way around that limitation (besides upgrading) is if there is a managed package available on the AppExchange that accomplishes your goals and is available for PE.
Alternatively, you might be able to purchase Workflow as an add on to PE, which would get you Outbound Messaging (which forces you to use the XML messaging of Workflow and may not fit your use case), but you could always throw together a proxy that it hits and converts to the API format of your other endpoint.